In the standard univariate situation, power depends on the size of the
effect. In the SPM setting, one would also have to consider the extent
of the effect. This is because the probability of max(t) to exceed the
significance threshold must depend on the number of voxels in which
the expectation of t is not zero, i.e. the null is false (each of
these voxels has a chance to provide the t for which max(t) is
overthreshold). The number of combinations is daunting, and the
usually speculative character of power calculations becomes even more
If one has a definite hypothesis on how large the violation of the
null might be, then one possibility is carry out Monte Carlo
simulations on artificially generated data. Even this wouldn't
replicate the SPM test, because the latter computes estimates of
smoothness from the residuals, but it would be a start.
A more pragmatic computation is based on the t values that are usually
enough to produce significant results. In my experience, one must
target a t value of at least about 5.
Dept. of Psychiatry
University of Ulm
Quoting Christian Gaser <[log in to unmask]>:
> Hi Vincent,
> G*Power is an excellent tool to estimate statistical power:
> I have also attached an example output for a two-sample T-test. For
> medium effects you
> need about 50 subjects in each group to obtain reasonable power
> (1-beta = 0.8).
> However, this is a power analysis of a single voxel (univariate
> power) using the well
> known formulas. The calculation might be too conservative in the
> case of detecting an
> effect in more than one voxel (mass univariate power). I have found
> only a few papers
> regarding this issue (Friston et al., NI 1996; Zarahn & Slifstein,
> NI 2001; Desmond &
> Glover, J Neurosci M 2001). After reading the papers I am still
> unsure about the right way
> to calculate power for VBM data, which should be equivalent to a
> second level analysis of
> fMRI data. What is the right way to correct the power calculation
> for mass univariate
> I guess this issue might be quite important for many people to estimate the
> sample size needed to detect effects with effect size d using alpha level p
> for mass univariate data with a given smoothness (or size of resels).
> Christian Gaser, Ph.D.
> Assistant Professor of Computational Neuroscience
> Department of Psychiatry
> Friedrich-Schiller-University of Jena
> Jahnstrasse 3, D-07743 Jena, Germany
> Tel: ++49-3641-934752 Fax: ++49-3641-934755
> e-mail: [log in to unmask]
> On Thu, 22 Jan 2009 14:56:56 +0800, dfwang <[log in to unmask]> wrote:
>> When doing VBM on two groups of subjects, how to assure the number
>> of participants is
> enough to conclusively identify brain abnormalities? How to do power
> calculation to
> determine the required numbers?
>> Thanks a lot.